New Modeling Tests for Shallow Water Waves

Citation

Permanent Link:: https://ufdc.ufl.edu/UFE0047492/00001

Material Information

Title:: New Modeling Tests for Shallow Water Waves
Creator:: Gravois, Uriah M
Place of Publication:: [Gainesville, Fla.]
Florida
Publisher:: University of Florida
Publication Date:: 2019
Language:: english
Physical Description:: 1 online resource (187 p.)

Thesis/Dissertation Information

Degree:: Doctorate ( Ph.D.)
Degree Grantor:: University of Florida
Degree Disciplines:: Coastal and Oceanographic Engineering
Civil and Coastal Engineering
Committee Chair:: Slinn,Donald Nicholas
Committee Co-Chair:: Olabarrieta Lizaso,Maitane
Committee Members:: Valle-Levinson,Arnoldo
Adams,Peter N
Rogers,William Erick

Subjects

Subjects / Keywords:: coastal -- waves -- wavewatchiii
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre:: bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Coastal and Oceanographic Engineering thesis, Ph.D.

Notes

Abstract:: The importance of ocean waves to commercial industry, military and recreational activities at sea is well established. This is evident in the existing global and regional wave observation networks and models used by weather forecast centers. Capabilities are being extended to support shallow water forecasts of coastal engineering significance for applications to shoreline change, coastal infrastructure risk, rip current prediction and wave energy assessment. To contribute towards improving coastal operational wave models, two test cases were set up and validated with extensive measured data from dedicated field experiments. The two validation test cases were selected where site specific processes exist that are known to influence the wave modeling framework. Specifically, test cases were set up in environments where shallow water, seabed material, and ocean current effects on waves are significant. The first test case is located in South East Florida in close proximity to the Gulf Stream and steep reefs of the continental shelf. This test case applies the SWAN (Simulating WAves Nearshore) wave model coupled with modeled ocean currents. The focus of the first case is to compare modeled results against a combination of in situ and remotely sensed high frequency radar observations. Bulk wave parameters are compared with observations to investigate the effect of wave current interaction, deep water wave direction, and shallow water. The second case is located in the Northern Gulf of Mexico on the muddy Atchafalaya shelf and uses exclusively the traditionally deep water wave model WaveWatchIII. The focus of the second test is to compare model results against is situ measured data at numerous locations. Results are quantified by skill metrics versus dimensionless wavenumber for different model wind-wave growth source terms and bottom frictions. Model data comparisons from both of the validation test cases indicated good skill. For the South East Florida case, comparisons with high frequency radar observations indicated that wave current coupling was significant and that including currents in the wave model improved the skill. Additionally, the nearshore wave height was influenced by offshore wave direction as well as wave-current interaction. For the mild sloping shallow Atchafalaya shelf, bottom friction parameter values were found to have the greatest influence on model skill. Difference in model skill for two wind input source terms was also evaluated. These results suggest that existing deep water wave model capabilities are adequate for weather forecast centers to develop operational coastal wave models. The findings highlight the usefulness of dedicated field experiments and remote sensing observations. The validation test cases applied to the coastal model frameworks exhibited good skill. ( en )
General Note:: In the series University of Florida Digital Collections.
General Note:: Includes vita.
Bibliography:: Includes bibliographical references.
Source of Description:: Description based on online resource; title from PDF title page.
Source of Description:: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:: Thesis (Ph.D.)--University of Florida, 2019.
Local:: Adviser: Slinn,Donald Nicholas.
Local:: Co-adviser: Olabarrieta Lizaso,Maitane.
Statement of Responsibility:: by Uriah M Gravois.

Record Information

Source Institution:: UFRGP
Rights Management:: Applicable rights reserved.
Classification:: LD1780 2019 ( lcc )

UFDC Membership

Aggregations:: University of Florida Theses & Dissertations

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Full Text

PAGE 6

Sbot

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)]TJ /F1 11.9552 Tf 7.314 0 Td[<0034007900580052004e0056>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 261.409 -591.235 Td[<0058>-500<0058>-500<0058>-500<0058>-500<0058>-499<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>]TJ ET BT /F1 11.9552 Tf 450.426 -591.235 Td[<005200650033>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 0 -615.143 Td[<002e0040006a>-736<00610046004200480048>-326<004b0032006900600042002b0062>-326<003700510060>-326<0062003f001c004800480051>26<0072>-325<0072>26<001c006900320060>-325<00710071006a>-326<0054001c006000690042001c0048>-326<0072>26<001c>27<0070>27<0032>-325<003f00320042003b003f>26<00690062>-325<007200420069003f>-326<004a006c002e0040004a006c005f0041>]TJ 27.497 -14.446 Td[<005100230062003200600070>54<001c006900420051004d0062>-326<001c0062>-326<003b00600051006d004d002f>-326<00690060006d0069003f002c>-434<0055002200680052>]TJ /F4 11.9552 Tf 187.023 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<003400790058006a00330056>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 261.409 -629.589 Td[<0058>-500<0058>-500<0058>-500<0058>-500<0058>-499<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>]TJ ET BT /F1 11.9552 Tf 450.426 -629.589 Td[<00520065004e>]TJ ET BT /F1 11.9552 Tf 231.071 -687.851 Td[<004e>]TJ ET Q

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)]TJ /F1 11.9552 Tf 7.314 0 Td[<003400790058006500640056>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 261.409 -26.401 Td[<0058>-500<0058>-500<0058>-500<0058>-500<0058>-499<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>-500<0058>]TJ ET BT /F1 11.9552 Tf 450.426 -26.401 Td[<005200640079>]TJ ET BT /F1 11.9552 Tf 228.142 -687.851 Td[<00520079>]TJ ET Q

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10

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max

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r2=0: =H 2g coshk(h+z) coshkhcos(kx)sin(t); Hgkh=2=TTk=2=LL2=gktanhkh:

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ktanhkhkh1khC=L TorC= k: =H 2g coshk(h+z) coshkhsin(kx)]TJ /F2 11.9552 Tf 11.955 0 Td[(t): TLh E=1 8gH2;

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F=ECg; Cg=@ @k=n k; n=1 2+kh sinh2kh: CgCn1 21FghCg=kg m3m s2m2 m s=J m2m s=W m: sin2 C2=sin1 C1; =0

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H2=H1KsKr=H1Cg1 Cg21 2cos1 cos21 2; KsKr E=IXi=1JXj=1E(fi;j)jfi: f E(fi)=JXj=1E(fi;j)j: E(j)=IXi=1E(fi;j)fi:

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kthmk=IXi=1(fi)kE(fi)i: m0Hs=4(m0)1 2: faverage=1 Tm01=m0 m1: fpeak=max(E(f)df):

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cm2=Hz=Degree0:2)]TJ /F4 11.9552 Tf 11.955 0 Td[(0:3Hz110)]TJ /F4 11.9552 Tf 11.901 0 Td[(1400:3)]TJ /F4 11.9552 Tf 11.902 0 Td[(0:35Hz175)]TJ /F4 11.9552 Tf 11.902 0 Td[(190

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mean=arctan0BBBBB@JXj=1 sinj IXi=1E(fi;j)fi!j! JXj=1 cosj IXi=1E(fi;j)fi!j!1CCCCCA: 00

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peak=arctan0BBBBB@JXj=1(sinj(E(fp;j)fp)j) JXj=1(cosj(E(fp;j)fp)j)1CCCCCA:

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1 2 1 21122 12 1b12b2 1122 r1=1 a0(a1)2 (b1)21 2 r2=1 a0(a2)2 (b2)21 2

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1=tan)]TJ /F5 7.9701 Tf 6.586 0 Td[(1b1 a1 2=1 2tan)]TJ /F5 7.9701 Tf 6.587 0 Td[(1b2 a2; 000 P=g(h+):

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Y(s)=NXj=1y(j)exp)]TJ /F2 11.9552 Tf 9.299 0 Td[(i2(j)]TJ /F4 11.9552 Tf 11.955 0 Td[(1)(s)]TJ /F4 11.9552 Tf 11.956 0 Td[(1) Ns=1:N;

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y(j)=1 NNXs=1Y(s)exp)]TJ /F2 11.9552 Tf 9.299 0 Td[(i2(j)]TJ /F4 11.9552 Tf 11.955 0 Td[(1)(s)]TJ /F4 11.9552 Tf 11.955 0 Td[(1) Nj=1:N: Kp=coshk(Ih) coshkh; h(Kp)2 (KP)210f)]TJ /F5 7.9701 Tf 6.586 0 Td[(4f)]TJ /F5 7.9701 Tf 6.586 0 Td[(5

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U10=Uz10 Z1 10: N(k;)=E(k;) : DN Dt=S ;

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Kp2 2

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@N @t+rx(Cg+U)N+rssN=S : (=2fr)!(=2fa)!=+)777(!k)777(!U: E(fr;)=@k @frE(k;)=2 CgE(k;): E(fa;)=@k @faE(k;)=2 Cg1+kU kCg)]TJ /F5 7.9701 Tf 6.587 0 Td[(1E(k;): E(fa;)=@fr @faE(fr;)= 1+)777(!k)777(!U kCg!)]TJ /F5 7.9701 Tf 6.587 0 Td[(1E(fr;):

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S=Sln+Sin+Snl+Sds+Sbot+Sdb+Str+Ssc+Sice+Smud+Sxx: Sln Sin Snl Sds Sbot Sdb Str Ssc Sice Sref Sxx inds

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bot inds =aCd(U10)2=aU2; U2=Cd(U10)2: Cd Cd104=8:058+0:967(U10))]TJ /F4 11.9552 Tf 11.955 0 Td[(0:016(U10)2:

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CDFAC=PU(observation) PU(model)2; Sbotbot Sbot(k;)=2)]TJ /F2 11.9552 Tf 34.662 8.088 Td[(n)]TJ /F4 11.9552 Tf 11.955 0 Td[(0:5 gdN(k;); )]TJ /F1 11.9552 Tf 11.212 0 Td[<001c00600032>-325<00690032006200690032002f>-326<0042004d>-326<0069003f0032>-326<00540060003200620032004d>26<0069>-325<0072>25<0051>1<00600046>-326<0055004c005100690032>-326<0069003f0032>-326<006d004d004200690062>-326<00510037>]TJ /F4 11.9552 Tf 252.828 0 Td[()]TJ /F1 11.9552 Tf 11.211 0 Td[<001c00600032>-326<004b>]TJ /F5 7.9701 Tf 29.267 4.339 Td[(23)-284(=0:067)-284(=0:038 )-332(=0:019

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0:6Hz0:25Hz

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#zh

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m01p

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#

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#

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# 10 10

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max m+1=Xm; X=1:1

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10

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CFL=max(Cg)t x; max(Cg)

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sm01p )]TJ /F1 11.9552 Tf 11.212 0 Td[<0034>-326<00790058006a0033>-326<0042002f0032004d>26<00690042007d0032002f>-325<0042004d>-326<0069003f0032>]TJ -331.634 -23.908 Td[<0062003f001c004800480051>26<0072>-325<0072>26<001c006900320060>-325<00690032006200690042004d003b>-326<005500610032002b006900420051004d>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 157.521 -289.383 Td[<00390058003900580052>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 181.599 -289.383 Td[<00560058>-434<004a0051>-27<002f003200480042004d003b>-326<006000320062006d004800690062>-326<0062003f0051>26<0072>-325<0051004d00480076>-326<0062006d0023006900480032>-326<002f0042007a003200600032004d002b00320062>-326<0042004d>-326<0023006d00480046>]TJ -181.599 -23.907 Td[<0072>26<001c>27<0070>27<0032>-325<0054001c0060001c004b00320069003200600062>-326<006d00620042004d003b>-326<0069003f0032>-326<002f0042007a003200600032004d>26<0069>-325<00710071006a>-326<00620051006d0060002b0032>-326<006900320060004b0062002d>-326<006100680039>-326<001c004d002f>-326<0061006800650058>-434<0068003f003200620032>-326<002f0042007a003200600032004d002b00320062>]TJ 0 -23.908 Td[<001c00600032>-326<005b006d001c004d>26<00690042007d0032002f>-325<006000320048001c006900420070>26<0032>-325<00690051>-326<0069003f003200420060>-326<00620046004200480048>-326<001c0069>-326<005400600032002f0042002b00690042004d003b>-326<0069003f0032>-326<004c002e0022002a>-326<005100230062003200600070>53<001c006900420051004d00620058>-433<00610046004200480048>-326<004b0032006900600042002b0062>]TJ 0 -23.908 Td[<002b001c0048002b006d0048001c00690032002f>-326<003700510060>-326<001c00480048>-326<0023006d0051>26<0076>-325<00480051>-27<002b001c006900420051004d0062>-326<003700510060>-326<00620042003b004d0042007d002b001c004d>26<0069>-325<0072>26<001c>27<0070>27<0032>-325<003f00320042003b003f>26<0069>-325<001c00600032>-326<00480042006200690032002f>-326<0042004d>-326<0068>81<001c002300480032>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 401.467 -361.106 Td[<003900400039>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 417.08 -361.106 Td[<002d>-325<00720042>-1<0069003f>]TJ -417.08 -23.908 Td[<001c>26<0070>27<00320060001c003b00320062>-325<0072>26<00320042003b003f>27<00690032002f>-325<0023>26<0076>-325<0069003f0032>-326<004d>26<006d004b>27<0023>-26<00320060>-326<00510037>-326<003f0051006d006000480076>-326<002f001c0069001c>-326<0054>-27<00510042004d>26<00690062>-325<003b00420070>26<0032004d>-325<001c0069>-326<0069003f0032>-326<0023>-27<0051006900690051004b>-326<00510037>-326<0069003f0032>-326<0069001c0023004800320058>]TJ 0 -23.908 Td[<0050004d>-326<001c>26<0070>27<00320060001c003b0032002d>-325<0069003f0032>-326<006100680039>-326<004b0051>-27<002f00320048>-326<0054>-27<00320060003700510060004b0032002f>-326<006200480042003b003f>26<006900480076>-325<0023>-27<003200690069003200600058>]TJ 23.384 -23.908 Td[<0041004d>-326<0054006000320054001c0060001c006900420051004d>-326<003700510060>-326<0069003f0032>-326<002f003200320054>-326<00690051>-326<0062003f001c004800480051>26<0072>-325<0072>26<001c006900320060>-325<002b0051004b0054001c0060004200620051004d0062>-326<0042004d>-326<00610032002b006900420051004d>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 375.416 -432.83 Td[<003900580039>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 390.384 -432.83 Td[<002d>-326<0069003f0032>-326<004c002e0022002a>]TJ -390.384 -23.907 Td[<0072>26<001c>27<0070>27<0032>-325<00620054>-27<0032002b00690060001c>-326<0072>26<003200600032>-325<0042004d>26<00690032003b0060001c00690032002f>-325<0023>-27<00320069>26<0072>27<00320032004d>-325<0079005800790065>-326<003e0078>-326<001c004d002f>-326<00790058006b0038>-326<003e00780058>-434<0068003f003200620032>-326<0054001c006000690042001c0048>-326<0072>26<001c>27<0070>27<0032>-325<003f00320042003b003f>26<00690062>]TJ 0 -23.908 Td[<001c00600032>-326<002f0032007d004d0032002f>-326<0069003f0032>-326<0062001c004b0032>-326<001c0062>-326<0069003f0032>-326<0023006d00480046>-326<0072>26<001c>27<0070>27<0032>-325<0054001c0060001c004b00320069003200600062>-326<005500610032002b006900420051004d>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 304.869 -480.645 Td[<006b0058006b0058006a>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 328.946 -480.645 Td[<0056002d>-326<00320074002b003200540069>-326<0069003f001c0069>-326<0069003f00320076>-326<002f0051>]TJ -328.946 -23.908 Td[<004d00510069>-326<0042004d002b0048006d002f0032>-326<0069003f0032>-326<003f0042003b003f>-326<003700600032005b006d0032004d002b0076>-326<0069001c00420048>-326<00510037>-326<0069003f0032>-326<00620054>-27<0032002b00690060006d004b0058>-434<0068003f00420062>-326<005400600051>-27<002b0032002f006d00600032>-326<0072>26<001c0062>-325<006d00620032002f>-326<00690051>-326<001c004800480051>26<0072>]TJ 0 -23.908 Td[<0062006d002300620032005b006d0032004d>26<0069>-325<0042004d>26<0069003200600040002b0051004b0054001c0060004200620051004d>-325<0023>-27<00320069>26<0072>27<00320032004d>-325<004b0051>-27<002f00320048>-326<00620046004200480048>-326<001c0069>-326<004c002e0022002a>-326<0023006d0051>26<0076>-325<005100230062003200600070>53<001c006900420051004d0062002d>-325<003f003200600032002d>-326<001c004d002f>]TJ 0 -23.908 Td[<0062003f001c004800480051>26<0072>-325<0072>26<001c006900320060>-325<00540060003200620062006d00600032>-326<00620032004d0062005100600062>-326<005500610032002b006900420051004d>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 204.589 -552.369 Td[<00390058006a00580052>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 228.667 -552.369 Td[<0056>-325<0069003f001c0069>-326<002b001c004d004d00510069>-326<004b0032001c0062006d00600032>-326<0069003f0032>-326<003f0042003b003f>-326<003700600032005b006d0032004d002b0076>]TJ -228.667 -23.908 Td[<0069001c00420048>-326<00510037>-326<0069003f0032>-326<0072>26<001c>27<0070>27<0032>-325<0032004d00320060003b0076>-326<002f0032004d006200420069>26<0076>-325<00620054>-27<0032002b00690060006d004b0058>-434<002a0051004b0054001c0060004200620051004d0062>-326<0023>-27<00320069>26<0072>27<00320032004d>-325<0069003f0032>-326<0037006d00480048>-326<001c004d002f>-326<0054001c006000690042001c0048>-326<0072>26<001c>27<0070>27<0032>]TJ 0 -23.907 Td[<003f00320042003b003f>26<00690062>-325<001c00600032>-326<003b00420070>26<0032004d>-325<0042004d>-326<00360042003b006d00600032>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 140.7 -600.184 Td[<003900400052006b>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 166.069 -600.184 Td[<003700510060>-326<001c00480048>-326<004c002e0022002a>-326<0023006d0051>26<007600620058>-433<0068003f003200620032>-326<002f0032004b0051004d006200690060001c00690032>-326<0069003f001c0069>-326<0054001c006000690042001c0048>-326<0072>26<001c>27<0070>27<0032>]TJ -166.069 -23.908 Td[<003f00320042003b003f>26<00690062>-325<00550023>-27<00320069>26<0072>27<00320032004d>-325<0079005800790065>-326<003e0078>-326<001c004d002f>-326<00790058006b0038>-326<003e00780056>-326<001c002b002b0051006d004d>26<0069>-325<003700510060>-326<004b005100620069>-326<00510037>-326<0069003f0032>-326<0072>26<001c>27<0070>27<0032>-325<0032004d00320060003b0076>81<002d>-325<003200620054>-27<0032002b0042001c004800480076>-326<003700510060>]TJ 0 -23.908 Td[<0048001c0060003b0032>-326<0072>26<001c>27<0070>27<00320062>-325<003f00320042003b003f>26<006900620058>-433<005f00320062006d004800690062>-326<003700510060>-326<002b0051004b0054001c00600042004d003b>-326<0054001c006000690042001c0048>-326<0072>26<001c>27<0070>27<0032>-325<003f00320042003b003f>26<00690062>-325<0023>-27<00320069>26<0072>27<00320032004d>-325<004b0051>-27<002f00320048>-326<001c004d002f>-326<004c002e0022002a>]TJ ET BT /F1 11.9552 Tf 228.142 -687.851 Td[<004e004e>]TJ ET Q

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sm01p

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sm01p

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sm01p

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s2s2s2 obs modobsmod

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obs modobsmod

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%

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3 2

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)]TJ /F1 11.9552 Tf 7.314 0 Td[<00340040007900580079006500640056>-325<0023>-27<0051006900690051004b>-326<003700600042002b006900420051>-1<004d>-326<002b0051004d007d0060004b0032002f>-326<006b0079>-326<004b>]TJ -250.363 -23.907 Td[<0072>26<001c0062>-325<002f003200320054>-326<0032004d0051006d003b003f>-326<00620051>-326<0069003f001c0069>-326<0023>-27<0051006900690051004b>-326<003700600042002b006900420051004d>-326<001c007a0032002b00690062>-326<0072>26<003200600032>-325<004b0042004d005100600058>-434<00680042004b0032>-326<006200320060004200320062>-326<001c0069>-326<0069003f0032>-326<00620051006d0069003f>26<0072>27<003200620069>]TJ 0 -23.908 Td[<001c004d002f>-326<00620051006d0069003f>-326<0032001c00620069>-326<002b00510060004d003200600062>-326<00510037>-326<0069003f0032>-326<003b00600042002f>-326<001c00600032>-326<0062003f0051>26<0072004d>-325<0042004d>-326<00360042003b006d00600032>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 282.333 -599.934 Td[<00390040006b006a>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 303.805 -599.934 Td[<0058>]TJ -280.421 -23.908 Td[<001b>26<0069>-325<0069003f0032>-326<0051007a0062003f005100600032>-326<0023>-27<0051006d004d002f001c00600076>-326<003700510060>-326<0069003f0032>-326<0052>-326<0046004b>-326<003b00600042002f002d>-326<002f001c0069001c>-326<003700600051004b>-326<0031004c002a>-326<0072>26<003200600032>-325<0060003200540048001c002b0032002f>-326<007200420069003f>]TJ -23.384 -23.908 Td[<002e0022002e0022006b>-326<002f001c0069001c>-326<0055006d00620032002f>-326<003700510060>-326<0069003f0032>-326<002f003200320054>-326<0072>26<001c006900320060>-325<003b00600042002f0056>-326<00690051>-326<0032004d0062006d00600032>-326<0062004b0051>-27<00510069003f>-326<00690060001c004d00620042006900420051004d>-326<001c004d002f>-326<002b0051004d00620042006200690032004d002b0076>81<0058>]TJ ET BT /F1 11.9552 Tf 225.213 -687.851 Td[<00520052006b>]TJ ET Q

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# )]TJ /F1 11.9552 Tf 11.211 0 Td[<0034>-326<00790058006a0033>-326<0023>-27<0051006900690051004b>-326<003700600042002b006900420051004d0058>-434<0068003f003200620032>-326<0042004d002b0048006d002f0032002f>-326<005200390039>-326<00620054>-27<0032002b00690060001c0048>-326<0054>-27<00510042004d>26<00690062>-325<003700600051004b>]TJ ET BT /F1 11.9552 Tf 225.213 -687.851 Td[<005200520065>]TJ ET Q

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=0:67 )]TJ /F1 11.9552 Tf 11.211 0 Td[<0070>53<001c0048006d00320062>-325<00550079002d>-326<007900580052004e002d>-326<00790058006a0033>-326<001c004d002f>-326<007900580065006400560058>-434<0068003f0032>]TJ -268.881 -23.908 Td[<0023>-27<0051006d004d002f001c00600076>-326<002b0051004d002f0042006900420051004d0062>-326<003700510060>-326<006100680039>-326<00550061006800650056>-326<0060006d004d0062>-326<0051004d>-326<003b00600042002f>-326<006a>-326<0072>26<003200600032>-325<0069001c0046>26<0032004d>-325<003700600051004b>-326<006100680039>-326<00550061006800650056>-326<0060006d004d0062>-326<0051004d>]TJ 0 -23.907 Td[<003b00600042002f0062>-326<0052>-326<001c004d002f>-326<006b0058>]TJ ET BT /F6 11.9552 Tf 0 -447.63 Td[<00390058006a00580039>-1000<0061003f001c004800480051>30<0072>-374<0071>93<001c006900320060>-374<00710071006a>-375<004a0051>-31<002f003200480042004d003b>-375<005f00320062006d004800690062>-375<001c004d002f>-375<006f>93<001c00480042002f001c006900420051004d>]TJ ET BT /F6 11.9552 Tf 0 -472.053 Td[<00390058006a0058003900580052>-1000<00680042004b0032>-375<006100320060004200320062>]TJ /F1 11.9552 Tf 23.384 -24.424 Td[<004a0051>-27<002f003200480032002f>-326<001c004d002f>-326<005100230062003200600070>26<0032002f>-325<00690042004b0032>-326<006200320060004200320062>-326<00510037>-326<0054001c006000690042001c0048>-326<0072>26<001c>27<0070>27<0032>-325<003f00320042003b003f>26<00690062>-325<00550079005800790065>-326<003e0078>-326<00690051>-326<00790058006b0038>-326<003e00780056>-326<001c0069>-326<001c00480048>]TJ -23.384 -23.907 Td[<0062003f001c004800480051>26<0072>-325<0062004200690032>-326<00540048001c0069003700510060004b0062>-326<0072>26<003200600032>-325<002b0051004b0054001c00600032002f>-326<006d00620042004d003b>-326<00620046004200480048>-326<004b0032006900600042002b00620058>-434<0068003f00420062>-326<001c004d001c00480076006200420062>-326<0062003f0051>26<0072>27<0032002f>-325<0069003f001c0069>-326<0069003f0032>]TJ 0 -23.908 Td[<0072>26<001c>27<0070>27<0032>-325<004b0051>-27<002f00320048>-326<00620042004b>26<006d0048001c006900420051004d0062>-325<007200420069003f>]TJ /F4 11.9552 Tf 151.663 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<003400790058006a0033>-326<0023>-27<0051006900690051004b>-326<003700600042002b006900420051004d>-326<0054>-27<00320060003700510060004b0032002f>-326<0023>-27<003200620069>-326<003700510060>-326<0023>-27<00510069003f>-326<0069003f0032>-326<006100680039>]TJ -158.977 -23.908 Td[<001c004d002f>-326<006100680065>-326<001c004d002f>-326<0069003f003200620032>-326<00690042004b0032>-326<006200320060004200320062>-326<001c00600032>-326<005400480051006900690032002f>-326<003700510060>-326<0032001c002b>26<003f>-325<00690060001c004d00620032002b0069>-326<0042004d>-326<00360042003b006d006000320062>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 362.373 -568.2 Td[<00390040006b0039>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 387.742 -568.2 Td[<00690051>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 402.052 -568.2 Td[<00390040006b0064>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 423.524 -568.2 Td[<0058>-434<004c005100690032>]TJ -423.524 -23.908 Td[<0069003f001c0069>-326<0072003f004200480032>-326<0069003f0032>-326<004b0051>-27<002f00320048>-326<00690042004b0032>-326<006200320060004200320062>-326<00420062>-326<003b00420070>26<0032004d>-325<003700510060>-326<0069003f0032>-326<0032004d>26<0069004200600032>-325<00620042004b>26<006d0048001c006900420051004d>-325<00480032004d003b0069003f002d>-326<0069003f0032>-326<002b0051004b0054001c0060004200620051004d0062>]TJ 0 -23.908 Td[<007200420069003f>-326<005100230062003200600070>53<001c006900420051004d0062>-325<002b001c004d>-326<0051004d00480076>-326<004b001c002f0032>-326<003700510060>-326<0062003f0051006000690032002f>-326<00690042004b00320062>-326<0072003f003200600032>-326<002f001c0069001c>-326<001c00600032>-326<001c>26<0070>54<001c00420048001c0023004800320058>-433<001b>-326<0062006d004b004b001c00600076>]TJ 0 -23.907 Td[<00510037>-326<0069003f0032>-326<00620046004200480048>-326<004b0032006900600042002b0062>-326<00420062>-326<003b00420070>26<0032004d>-325<0042004d>-326<0068>81<001c002300480032>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 187.134 -639.923 Td[<0039004000520079>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 212.503 -639.923 Td[<007200420069003f>-326<0032001c002b>26<003f>-325<00620069001c006900420051004d>-326<0072>26<00320042003b003f>27<00690032002f>-325<0023>26<0076>-325<0069003f0032>-326<004d>26<006d004b>27<0023>-26<00320060>-326<00510037>]TJ ET BT /F1 11.9552 Tf 225.213 -687.851 Td[<005200520033>]TJ ET Q

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)]TJ /F1 11.9552 Tf 11.212 0 Td[<0054001c0060001c004b00320069003200600062>-325<006d00620032002f002d>-326<001c004d002f>-326<003700510060>-326<0069003f0032>-326<006100680039>-326<001c004d002f>-326<006100680065>-326<0062>-1<0051006d0060002b0032>-326<006900320060004b00620058>-434<0053>26<001c004200600062>-325<00510037>]TJ -102.92 -23.908 Td[<0069003f003200620032>-326<00540048005100690062>-326<003700510060>-326<00230042001c0062>-326<001c004d002f>-326<004d00510060004b001c0048004200780032002f>-326<00230042001c0062>-326<0042004d>-326<00360042003b006d006000320062>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 262.559 -203.733 Td[<00390040006b0033>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 287.928 -203.733 Td[<001c004d002f>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 310.691 -203.733 Td[<00390040006b004e>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 332.162 -203.733 Td[<002d>-326<00600051>-27<00510069>-326<004b0032001c004d>-326<0062005b006d001c00600032>-326<00320060006000510060>]TJ -332.162 -23.908 Td[<0042004d>-326<00360042003b006d00600032>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 50.558 -227.641 Td[<00390040006a0079>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 75.927 -227.641 Td[<001c004d002f>-326<004d00510060004b001c0048004200780032002f>-326<00600051>-27<00510069>-326<004b0032001c004d>-326<0062005b006d001c00600032002f>-326<00320060006000510060>-326<0042004d>-326<00360042003b006d006000320062>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 341.894 -227.641 Td[<00390040006a0079>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 367.263 -227.641 Td[<001c004d002f>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 390.025 -227.641 Td[<00390040006a0052>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 411.497 -227.641 Td[<002d>-325<001c004d002f>]TJ -411.497 -23.908 Td[<002b00510060006000320048001c006900420051004d>-326<002b0051>-27<0032007b002b00420032004d>26<0069>-325<0042004d>-326<00360042003b006d00600032>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 163.726 -251.549 Td[<00390040006a006b>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 185.198 -251.549 Td[<0058>-434<0068003f003200620032>-326<00540048005100690062>-326<002b0051004d00620042006200690032004d>26<006900480076>-325<0062003f0051>26<0072>-325<0069003f001c0069>]TJ /F4 11.9552 Tf 189.234 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<003400790058006a0033>-326<0023>-27<0051006900690051004b>]TJ -381.746 -23.908 Td[<003700600042002b006900420051004d>-326<003f001c0062>-326<0069003f0032>-326<0062004b001c00480048003200620069>-326<00230042001c0062>-326<001c004d002f>-326<0060004b00620032002d>-326<001c004d002f>-326<0069003f0032>-326<0048001c0060003b003200620069>-326<002b00510060006000320048001c006900420051004d>-326<002b0051>-27<0032007b002b00420032004d>26<006900620058>]TJ ET BT /F1 11.9552 Tf 0 -302.963 Td[<0068>81<001c002300480032>-325<00390040005200790058>-434<001b>108<0070>27<00320060001c003b0032>-325<00620046004200480048>-326<004b0032006900600042002b0062>-326<003700510060>-326<0062003f001c004800480051>26<0072>-325<0072>26<001c006900320060>-325<00710071006a>-326<0054001c006000690042001c0048>-326<0072>26<001c>27<0070>27<0032>-325<003f00320042003b003f>26<00690062>-325<007200420069003f>]TJ 62.103 -14.446 Td[<004a006d002f0040004a006c005f0041>-326<005100230062003200600070>53<001c006900420051004d0062>-325<001c0062>-326<003b00600051006d004d002f>-326<00690060006d0069003f0058>-434<0053>26<001c006000690042001c0048>-325<0072>26<001c>27<0070>27<0032>-325<003f00320042003b003f>26<0069>-325<00420062>-326<002b0051004b0054006d00690032002f>]TJ 0 -14.446 Td[<0023>-27<00320069>26<0072>27<00320032004d>-325<003700600032005b006d0032004d002b004200320062>-326<0079005800790065>-326<00690051>-326<00790058006b0038>-326<003e00780058>-434<0036>81<00510060>-325<002f0032007d004d0042006900420051004d>-326<00510037>-326<00620046004200480048>-326<004b0032006900600042002b>-326<002f0032007d004d0042006900420051004d0062>]TJ 0 -14.446 Td[<00600032003700320060>-326<00690051>-326<001b00540054>-27<0032004d002f00420074>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 157.039 -346.301 Td[<001b>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 165.814 -346.301 Td[<0058>]TJ ET q .3985 w 0 -350.834 m 418.629 -350.834 l S Q BT /F4 11.9552 Tf 5.978 -361.726 Td[()]TJ /F1 11.9552 Tf 32.781 0 Td[<004f>-325<00510037>-326<005100230062>]TJ ET q .4782 w 99.38 -351.75 m 115.499 -351.75 l S Q BT /F2 11.9552 Tf 99.38 -361.726 Td[(obs modobsmod

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)]TJ /F1 11.9552 Tf 7.315 0 Td[<00340079>-325<001c0062>]TJ -364.388 -14.446 Td[<006900600042001c004d003b004800320062002d>]TJ /F4 11.9552 Tf 50.798 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<0034007900580052004e>-326<001c0062>-326<0062005b006d001c006000320062002d>]TJ /F4 11.9552 Tf 92.88 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<003400790058006a0033>-326<001c0062>-326<002b006000510062006200320062002d>-326<001c004d002f>]TJ /F4 11.9552 Tf 112.773 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<00340079005800650064>-326<001c0062>-326<00540048006d0062>-326<00620076004b>26<0023>-26<0051004800620058>]TJ ET q .95157 0 0 .95157 .299 -25.833 cm q 1 0 0 1 6.176 -533.413 cm /Fm178 Do Q Q BT /F8 9.9626 Tf 105.838 -547.858 Td[<0055001c0056>]TJ ET q .95157 0 0 .95157 11.427 -25.833 cm q 1 0 0 1 235.949 -533.413 cm /Fm179 Do Q Q BT /F8 9.9626 Tf 335.331 -547.858 Td[<005500230056>]TJ ET BT /F1 11.9552 Tf 0 -575.405 Td[<00360042003b006d00600032>-326<00390040006b004e0058>-434<004c00230042001c0062>-326<0070>26<003200600062006d0062>-325<0046003f>-326<003700510060>-326<0062003f001c004800480051>26<0072>-325<0072>26<001c006900320060>-325<00710071006a>-326<00620042004b>26<006d0048001c006900420051004d0062>-325<001c0056>-326<006100680039>-326<0042004d>-326<00600032002f>-326<001c004d002f>-326<00230056>]TJ 66.825 -14.446 Td[<006100680065>-326<0042004d>-326<00230048001c002b>26<00460058>-433<00220051006900690051004b>-326<003700600042002b006900420051004d>-326<0054001c0060001c004b0032006900320060>-326<0070>53<001c0048006d00320062>-325<001c00600032>-326<0062003f0051>26<0072004d>-325<0023>26<0076>-325<0062003f001c0054>-27<0032>-326<001c004d002f>]TJ 0 -14.446 Td[<002b0051004800510060002d>-326<007200420069003f>]TJ /F4 11.9552 Tf 58.533 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<00340079>-326<001c0062>-326<006900600042001c004d003b004800320062002d>]TJ /F4 11.9552 Tf 84.033 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<0034007900580052004e>-326<001c0062>-326<0062005b006d001c006000320062002d>]TJ /F4 11.9552 Tf 92.88 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<003400790058006a0033>-326<001c0062>-326<002b006000510062006200320062002d>-326<001c004d002f>]TJ /F4 11.9552 Tf -257.388 -14.446 Td[()]TJ /F1 11.9552 Tf 7.315 0 Td[<00340079005800650064>-325<001c0062>-326<00540048006d0062>-326<00620076004b>26<0023>-26<0051004800620058>]TJ ET BT /F1 11.9552 Tf 225.213 -687.851 Td[<0052006b0039>]TJ ET Q

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)]TJ /F1 11.9552 Tf 7.314 0 Td[<00340079>-326<001c0062>-326<006900600042001c004d003b004800320062002d>]TJ /F4 11.9552 Tf 84.033 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<0034007900580052004e>-326<001c0062>-326<0062005b006d001c006000320062002d>]TJ /F4 11.9552 Tf 92.88 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<003400790058006a0033>-326<001c0062>-326<002b006000510062006200320062002d>-326<001c004d002f>]TJ /F4 11.9552 Tf -257.388 -14.446 Td[()]TJ /F1 11.9552 Tf 7.315 0 Td[<00340079005800650064>-325<001c0062>-326<00540048006d0062>-326<00620076004b>26<0023>-26<0051004800620058>]TJ ET q .95157 0 0 .95157 .299 -26.008 cm q 1 0 0 1 6.176 -537.024 cm /Fm182 Do Q Q BT /F8 9.9626 Tf 105.838 -551.47 Td[<0055001c0056>]TJ ET q .95157 0 0 .95157 11.427 -26.008 cm q 1 0 0 1 235.949 -537.024 cm /Fm183 Do Q Q BT /F8 9.9626 Tf 335.331 -551.47 Td[<005500230056>]TJ ET BT /F1 11.9552 Tf 0 -579.016 Td[<00360042003b006d00600032>-326<00390040006a00520058>-434<004c0060004b00620032>-326<0070>26<003200600062006d0062>-325<0046003f>-326<003700510060>-326<0062003f001c004800480051>26<0072>-325<0072>26<001c006900320060>-325<00710071006a>-326<00620042004b>26<006d0048001c006900420051004d0062>-325<001c0056>-326<006100680039>-326<0042004d>-326<00600032002f>-326<001c004d002f>-326<00230056>]TJ 66.825 -14.446 Td[<006100680065>-326<0042004d>-326<00230048001c002b>26<00460058>-433<00220051006900690051004b>-326<003700600042002b006900420051004d>-326<0054001c0060001c004b0032006900320060>-326<0070>53<001c0048006d00320062>-325<001c00600032>-326<0062003f0051>26<0072004d>-325<0023>26<0076>-325<0062003f001c0054>-27<0032>-326<001c004d002f>]TJ 0 -14.446 Td[<002b0051004800510060002d>-326<007200420069003f>]TJ /F4 11.9552 Tf 58.533 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<00340079>-326<001c0062>-326<006900600042001c004d003b004800320062002d>]TJ /F4 11.9552 Tf 84.033 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<0034007900580052004e>-326<001c0062>-326<0062005b006d001c006000320062002d>]TJ /F4 11.9552 Tf 92.88 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<003400790058006a0033>-326<001c0062>-326<002b006000510062006200320062002d>-326<001c004d002f>]TJ /F4 11.9552 Tf -257.388 -14.446 Td[()]TJ /F1 11.9552 Tf 7.315 0 Td[<00340079005800650064>-325<001c0062>-326<00540048006d0062>-326<00620076004b>26<0023>-26<0051004800620058>]TJ ET BT /F1 11.9552 Tf 225.213 -687.851 Td[<0052006b0038>]TJ ET Q

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)]TJ /F1 11.9552 Tf 7.314 0 Td[<00340079>-326<001c0062>-326<006900600042001c004d003b004800320062002d>]TJ /F4 11.9552 Tf 84.033 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<0034007900580052004e>-326<001c0062>-326<0062005b006d001c006000320062002d>]TJ /F4 11.9552 Tf 92.88 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<003400790058006a0033>-326<001c0062>-326<002b006000510062006200320062002d>]TJ -313.051 -14.445 Td[<001c004d002f>]TJ /F4 11.9552 Tf 22.763 0 Td[()]TJ /F1 11.9552 Tf 7.314 0 Td[<00340079005800650064>-326<001c0062>-326<00540048006d0062>-326<00620076004b>26<0023>-26<0051004800620058>]TJ ET BT /F1 11.9552 Tf 0 -308.275 Td[<002f003200540069003f>-326<0046003f>-326<0023>-27<0032002b0051004b00320062>-326<002f0051004b0042004d001c00690032002f>-326<0023>26<0076>-325<0070>26<003200600076>-325<0048001c0060003b0032>-326<002f003200540069003f0062>-326<003f>-326<003700510060>-326<002f003200320054>-326<0072>26<001c006900320060>-325<004c002e0022002a>-326<0023006d0051>26<007600620058>-433<0041004d006200690032001c002f002d>]TJ 0 -23.907 Td[<0069003f0032>-326<0060001c006900420051>-326<004d>-326<0072>26<001c0062>-325<006d00620032002f>-326<001c0062>-326<004b0032001c0062006d00600032>-326<00510037>-326<0069003f0032>-326<0072>26<001c006900320060>-325<002f003200540069003f0058>-434<005f0032002b001c00480048>-326<003700600051004b>-326<0069003f0032>-326<006000320070004200320072>-326<00510037>-326<0069003f0032005100600076>]TJ 0 -23.908 Td[<0042004d>-326<002a003f001c0054006900320060>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 59.178 -356.09 Td[<006b>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 68.934 -356.09 Td[<00550031005b006d001c006900420051004d0062>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 128.673 -356.09 Td[<006b00400039>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 144.287 -356.09 Td[<002d>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 151.436 -356.09 Td[<006b00400033>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 170.947 -356.09 Td[<001c004d002f>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 193.71 -356.09 Td[<006b0040004e>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 209.323 -356.09 Td[<0056>-326<004d>-326<00420062>-326<0069003f0032>-326<0060001c006900420051>-326<00510037>-326<0069003f0032>-326<0054003f001c00620032>-326<00620054>-27<00320032002f>-326<002a>-326<001c004d002f>-326<0069003f0032>]TJ -209.323 -23.908 Td[<003b00600051006d0054>-326<0070>26<003200480051>-26<002b00420069>26<0076>-325<002a>]TJ /F3 7.9701 Tf 84.882 -1.793 Td[(g

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)]TJ /F1 11.9552 Tf 11.211 0 Td[<0023>-27<0051006900690051004b>-326<003700600042002b006900420051004d>-326<0054001c0060001c004b00320069003200600058>]TJ -317.718 -23.908 Td[<00610054>-27<0032002b00690060001c0048>-326<002f001c0069001c>-326<001c0069>-326<0054>-27<00510042004d>26<0069>-325<0051006d00690054006d00690062>-326<003700600051004b>-326<0069003f0032>-326<004b0051>-27<002f00320048>-326<0072>26<003200600032>-325<005400600051>-27<002b0032006200620032002f>-326<0042004d>-326<0069003f0032>-326<0062001c004b0032>-326<004b001c004d004d00320060>-326<001c0062>-326<0069003f0032>]TJ 0 -23.907 Td[<005100230062003200600070>53<001c006900420051004d00620058>-433<00610046004200480048>-326<004b0032006900600042002b0062>-326<0023>-27<00320069>26<0072>27<00320032004d>-325<0069003f0032>-326<004b0051>-27<002f003200480032002f>-326<001c004d002f>-326<005100230062003200600070>26<0032002f>-325<0072>26<001c>27<0070>27<00320062>-325<003700510060>-326<0032001c002b>26<003f>-325<0062004200690032>-326<0072>26<003200600032>]TJ 0 -23.908 Td[<005400480051006900690032002f>-326<0070>26<003200600062006d0062>-325<0046003f002d>-326<002f0032004b0051004d006200690060001c00690042004d003b>-326<0069003f0032>-326<00620032004d0062004200690042007000420069>26<0076>-325<00510037>-326<004b0051>-27<002f00320048>-326<00620046004200480048>-326<00690051>-326<0069003f0032>]TJ /F4 11.9552 Tf 355.798 0 Td[()]TJ /F1 11.9552 Tf 11.211 0 Td[<0054001c0060001c004b0032006900320060>-326<003700510060>-326<0062004b001c00480048>]TJ -367.009 -23.908 Td[<0046003f>-326<0070>53<001c0048006d003200620058>-433<0050004d>-326<001c>26<0070>27<00320060001c003b0032>-325<0069003f0032>-326<0072>26<001c>27<0070>27<0032>-325<004b0051>-27<002f00320048>-326<002b0051004d007d003b006d0060001c006900420051004d>-326<007200420069003f>-326<006100680039>-326<0072>26<001c0062>-325<0051004d00480076>-326<004b001c0060003b0042004d001c004800480076>-326<0023>-27<00320069006900320060>]TJ 0 -23.908 Td[<0069003f001c004d>-326<003700510060>-326<006100680065>-326<0042004d>-326<0023>-27<00510069003f>-326<0062003f001c004800480051>26<0072>-325<001c004d002f>-326<002f003200320054>-326<0072>26<001c0069003200600058>-433<0068003f00420062>-326<00420062>-326<0069003f0032>-326<007d006000620069>-326<002b0051004b0054001c0060004200620051004d>-326<0023>-27<00320069>26<0072>27<00320032004d>-325<0069003f0032>]TJ 0 -23.908 Td[<002f001c0069001c>-326<001c004d002f>-326<001c>-326<003a006d00480037>-326<00510037>-326<004a003200740042002b0051>-326<0062002b001c00480032>-326<0072>26<001c>27<0070>27<0032>-325<004b0051>-27<002f003200480058>-434<005300600032007000420051006d0062>-326<0072>26<001c>27<0070>27<0032>-325<004b0051>-27<002f003200480062>-326<003f001c>26<0070>27<0032>-325<001c00480048>-326<0023>-27<00320032004d>-326<003700510060002b0032002f>-326<001c0069>]TJ 0 -23.908 Td[<0069003f003200420060>-326<0023>-27<0051006d004d002f001c00600076>-326<0023>26<0076>-325<003200420069003f00320060>-326<004c002e0022002a>-326<002f001c0069001c>-326<00510060>-326<005100230062003200600070>53<001c006900420051004d>-325<0069001c0046>26<0032004d>-325<001c0069>-326<0069003f0032>-326<002f003200320054>-326<004a006d002f0040004a006c005f0041>-326<006200420069003200620058>]TJ 0 -23.907 Td[<0068003f0032>-326<001c0054005400600051001c002b>26<003f>-325<006d00620032002f>-326<003f003200600032>-326<00510037>-326<002f0060004200700042004d003b>-326<0069003f0032>-326<004b0051>-27<002f003200480062>-326<007200420069003f>-326<0023001c00620042004d>-326<0062002b001c00480032>-326<00720042004d002f>-326<003700510060002b0042004d003b>-326<0051004d00480076>81<002d>-325<00420062>-326<004b005100600032>]TJ 0 -23.908 Td[<0069001c00420048005100600032002f>-326<00690051>-326<0069003f0032>-326<004c007100530061>-326<001c004d002f>-326<0069003f0032>-326<002a0050>26<001b004a00530061>-325<004b0051>-27<002f003200480042004d003b>-326<001c0054005400600051001c002b>26<003f003200620058>]TJ 23.384 -23.908 Td[<0068003f0032>-326<00620046004200480048>-326<004b0032006900600042002b0062>-326<003700600051004b>-326<0069003f0032>-326<002f003200320054>-326<001c004d002f>-326<0062003f001c004800480051>26<0072>-325<0072>26<001c006900320060>-325<002b001c006200320062>-326<0072>26<003200600032>-325<002b00600051006200620040002b0051004b0054001c00600032002f0058>-434<0068003f0032>]TJ -23.384 -23.908 Td[<002f003200320054>-326<0072>26<001c006900320060>-325<004c002e0022002a>-326<0023006d0051>26<0076>-325<002f003200540069003f0062>-326<0072>26<003200600032>-325<004b>26<006d002b>27<003f>-325<003b00600032001c006900320060>-326<0069003f001c004d>-326<0069003f0032>-326<004b0032001c004d>-326<0072>26<001c>27<0070>27<003200480032004d003b0069003f0062002d>-325<0069003f>26<006d0062>-325<0046003f>]TJ 0 -23.908 Td[<0072>26<001c0062>-325<0140>]TJ /F2 11.9552 Tf 32.901 0 Td[(=2

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x=1 nnXi=1(xi) M)]TJ ET q .4782 w 242.957 -171.963 m 252.228 -171.963 l S Q BT /F2 11.9552 Tf 242.957 -181.806 Td[(O M)]TJ ET q .4782 w 242.957 -235.601 m 252.228 -235.601 l S Q BT /F2 11.9552 Tf 242.957 -245.444 Td[(O O 2x= (x)]TJ ET q .4782 w 252.772 -318.437 m 259.424 -318.437 l S Q BT /F2 11.9552 Tf 252.772 -325.258 Td[(x)2 x=q (x)]TJ ET q .4782 w 258.75 -390.163 m 265.402 -390.163 l S Q BT /F2 11.9552 Tf 258.75 -396.984 Td[(x)2 cov(x;y)= (x)]TJ ET q .4782 w 253.13 -461.889 m 259.782 -461.889 l S Q BT /F2 11.9552 Tf 253.13 -468.71 Td[(x)(y)]TJ ET q .4782 w 289.635 -461.889 m 295.772 -461.889 l S Q BT /F2 11.9552 Tf 289.635 -468.71 Td[(y) rmse=q (M)]TJ /F2 11.9552 Tf 11.955 0 Td[(O)2 nrmse=s P(M)]TJ /F2 11.9552 Tf 11.955 0 Td[(O)2 P(O)2

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r=cov(M;O) p 2M2O

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(1;1)(2;2))496(!i1;2=cos(1;2)cos(1;2) )425(!j1;2=cos(1;2)sin(1;2) )321(!k1;2=sin(1;2) =arccos()777(!i1)777(!i2+)777(!j1)777(!j2+)777(!k1)777(!k2 360)(40;003:2km) 1=arctansin(2)]TJ /F2 11.9552 Tf 11.955 0 Td[(1)cos(2) cos(1)sin(2))]TJ /F4 11.9552 Tf 11.956 0 Td[(sin(1)cos(2)cos(2)]TJ /F2 11.9552 Tf 11.955 0 Td[(1) (2;2)(1;1)(1)()2=arcsin(sin(1)cos()+cos(1)sin()cos(1)) 2=1+arctan(sin()sin()cos(1) cos())]TJ /F4 11.9552 Tf 11.955 0 Td[(sin(1)sin(2)); (=d=R)dR

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s

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s

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s

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m01p

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m01p

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m01p

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sm01p

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sm01p

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sm01p

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sm01p

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sm01p

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sm01p

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sm01p

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sm01p

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obs modobsmod

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)]TJ /F1 11.9552 Tf 7.314 0 Td[<0034007900580052004e00560058>-434<0053>26<001c006000690042001c0048>-325<0072>26<001c>27<0070>27<0032>-325<003f00320042003b003f>26<0069>-325<00420062>-326<002b0051004b0054006d00690032002f>]TJ -194.336 -14.446 Td[<0023>-26<00320069>26<0072>27<00320032004d>-325<003700600032005b006d0032004d002b004200320062>-326<0079005800790065>-326<00690051>-326<00790058006b0038>-326<003e00780058>-435<0036>81<00510060>-325<002f0032007d004d0042006900420051004d>-326<00510037>-326<00320060006000510060>-326<004b0032006900600042002b>-326<002f0032007d004d0042006900420051004d0062>]TJ 0 -14.446 Td[<00600032003700320060>-325<00690051>-326<001b00540054>-27<0032004d002f00420074>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 154.266 -66.275 Td[<001b>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 163.041 -66.275 Td[<0058>]TJ ET q .3985 w 0 -70.808 m 462.935 -70.808 l S Q BT /F1 11.9552 Tf 5.978 -81.701 Td[<004c001c004b0032>-1231<00610068>-1490<004f>-326<00510037>-326<005100230062>]TJ ET q .4782 w 143.686 -71.725 m 159.805 -71.725 l S Q BT /F2 11.9552 Tf 143.686 -81.701 Td[(obs modobsmod

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)]TJ /F1 11.9552 Tf 7.314 0 Td[<003400790058006a003300560058>-434<0053>26<001c006000690042001c0048>-325<0072>26<001c>27<0070>27<0032>-325<003f00320042003b003f>26<0069>-325<00420062>-326<002b0051004b0054006d00690032002f>]TJ -194.336 -14.446 Td[<0023>-26<00320069>26<0072>27<00320032004d>-325<003700600032005b006d0032004d002b004200320062>-326<0079005800790065>-326<00690051>-326<00790058006b0038>-326<003e00780058>-435<0036>81<00510060>-325<002f0032007d004d0042006900420051004d>-326<00510037>-326<00320060006000510060>-326<004b0032006900600042002b>-326<002f0032007d004d0042006900420051004d0062>]TJ 0 -14.446 Td[<00600032003700320060>-325<00690051>-326<001b00540054>-27<0032004d002f00420074>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 154.266 -66.275 Td[<001b>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 163.041 -66.275 Td[<0058>]TJ ET q .3985 w 0 -70.808 m 462.935 -70.808 l S Q BT /F1 11.9552 Tf 5.978 -81.701 Td[<004c001c004b0032>-1231<00610068>-1490<004f>-326<00510037>-326<005100230062>]TJ ET q .4782 w 143.686 -71.725 m 159.805 -71.725 l S Q BT /F2 11.9552 Tf 143.686 -81.701 Td[(obs modobsmod

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)]TJ /F1 11.9552 Tf 7.314 0 Td[<0034007900580065006400560058>-434<0053>26<001c006000690042001c0048>-325<0072>26<001c>27<0070>27<0032>-325<003f00320042003b003f>26<0069>-325<00420062>-326<002b0051004b0054006d00690032002f>]TJ -194.336 -14.446 Td[<0023>-26<00320069>26<0072>27<00320032004d>-325<003700600032005b006d0032004d002b004200320062>-326<0079005800790065>-326<00690051>-326<00790058006b0038>-326<003e00780058>-435<0036>81<00510060>-325<002f0032007d004d0042006900420051004d>-326<00510037>-326<00320060006000510060>-326<004b0032006900600042002b>-326<002f0032007d004d0042006900420051004d0062>]TJ 0 -14.446 Td[<00600032003700320060>-325<00690051>-326<001b00540054>-27<0032004d002f00420074>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 154.266 -66.275 Td[<001b>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 163.041 -66.275 Td[<0058>]TJ ET q .3985 w 0 -70.808 m 462.935 -70.808 l S Q BT /F1 11.9552 Tf 5.978 -81.701 Td[<004c001c004b0032>-1231<00610068>-1490<004f>-326<00510037>-326<005100230062>]TJ ET q .4782 w 143.686 -71.725 m 159.805 -71.725 l S Q BT /F2 11.9552 Tf 143.686 -81.701 Td[(obs modobsmod